April 27, 2015

Homework Help: Physics

Posted by Mehreen on Tuesday, April 5, 2011 at 6:11pm.

In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual fact, the outer layers of rock have lower density than the inner core of molten iron.)

1. Using the uniform-density approximation, find an expression for the amount of energy required to move a mass m from the center of the Earth to the surface.

I wanted to do the following:
We know from the given information that F (from the gravitational field strength) = mg(r/R)
Then using W=Fd, you could get (mg(r/R))(R), where R cancels out and W=mgr. But Force isn't a constant. So how would you solve this problem then?

2. Calculate the ratio of the energy you found, to the energy required to move the mass from Earth's surface to a very large distance away.

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